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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 017, 29 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.017 (Mi sigma1700) 		 
Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian

Masayuki Aino

RIKEN, Center for Advanced Intelligence Project AIP, 1-4-1 Nihonbashi, Tokyo 103-0027, Japan
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DOI: https://doi.org/10.3842/SIGMA.2021.017
Abstract: We show a Gromov–Hausdorff approximation to the product of the standard spheres $S^{n-p}\times S^p$ for Riemannian manifolds with positive Ricci curvature under some pinching condition on the eigenvalues of the Laplacian acting on functions and forms.
Keywords: Gromov–Hausdorff distance, Lichnerowicz–Obata estimate, parallel $p$-form.
Funding agency
This work was supported by RIKEN Special Postdoctoral Researcher Program.
Received: July 17, 2020; in final form February 7, 2021; Published online February 24, 2021
Bibliographic databases:
Document Type: Article
MSC: 53C20, 58J50
Language: English
Citation: Masayuki Aino, “Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian”, SIGMA, 17 (2021), 017, 29 pp.
Citation in format AMSBIB
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